Hair particle system rotation is not working
I have come across a work-around for this issue. When experimenting, I placed hairs particles on other objects in the scene and notice that they lacked this issue (their orientation axis could be fully manipulated and were properly aligned to begin with), so I concluded that the issue was in the object itself. Thus, my solution was to replace the object.

I separated the &quot;vines&quot; from the &quot;log&quot; by selecting everything in edit mode with A and then using P followed by selecting loose parts.
Then I created two large half-pipe cylinders around the log object (one above and one below) and used the shrinkwrap modifier with the target being the log. I had to select the project option because any other option resulted in issues stemming from the (presumably corrupted) normal data. This is also the reason for making them be half-pipes instead of full cylinders, as I could not get a full cylinder to work correctly with the project option.
After applying the shrinkwrap modifier, I had a replacement object with proper behavior, and was able to produce the images below.

Note that if you find this question because you have a similar issue, this might not work for complex models. I am lucky because my object was essentially just a deformed cylinder.